Open AccessEight-vertex model over Grassmann algebra
Author(s) -
T. K. Kassenova,
Pyotr Tsyba,
Olga Razina
Publication year - 2019
Publication title -
journal of physics. conference series
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.21
H-Index - 85
eISSN - 1742-6596
pISSN - 1742-6588
DOI - 10.1088/1742-6596/1391/1/012035
Subject(s) - mathematics , mathematical physics , vertex model , vertex (graph theory) , lattice (music) , transfer matrix , generalization , pure mathematics , quantum , algebra over a field , quantum mechanics , physics , mathematical analysis , combinatorics , graph , computer science , acoustics , computer vision
An eight-vertex model on a square lattice over a Grassmann algebra is investigated using an equation that is a three-dimensional generalization of the Yang-Baxter equation. Anticommuting quantum spin systems are studied, where the quasiclassical limit leads to some abstract classical physics with anticommuting variables. The solution of the quantum Yang-Baxter equation is the R - matrix, which corresponds to the transfer R - matrix of the eight-vertex model of statistical mechanics.